20. If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?
Ⅰ. x = y
Ⅱ. y = 1
Ⅲ. x and y are prime integers.
(A) None
(B) Ⅰ only
(C) Ⅱonly
(D) Ⅲonly
(E) Ⅰand Ⅲ

I got A.

You can pick numbers that contradict all three statements.
What is the OA?

My answer is B.

3x/y = 3*(x/y) <- prime number that is greater than 2.
if x and y are equal than the eqn becomes 3 * (1) = 3 (prime number greater than 2)

Since we are looking for an integer (all prime numbers are integers) and y != 3 than x must equal y.

The answer is A - Other than picking numbers, is there any option here ? I spent more than 2 minutes on this and fell for the wrong answer.

-pradeep
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Ans must be B

3x/y and if x=y then ans is 3 and 3 is prime number, which is greater than 2. so ans must be B. Please post OA.

If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true?
Ⅰ. x = y
Ⅱ. y = 1
Ⅲ. x and y are prime integers.
(A) None
(B) Ⅰ only
(C) Ⅱonly
(D) Ⅲonly
(E) Ⅰand Ⅲ

Answer to this question is A. None of the statements (I,II,III) must be true.

This Q. can be solved by number plugging in a minute but it's quite tricky, so let's generalize it so to understand the concept, as there are many similar problems in GMAT:

Q. says that: y≠3 and that 3x/y IS a prime integer. Then it asks which of the statements MUST be true?

First note that it's not stated that x and y are integers or positive/negative.

Generally, the expression 3x/y is always prime in two cases:

When x is a multiple of prime and y is same multiple of three: x=pn and y=3n (p prime >2, n ANY number but 1), so we have 3(pn)/3n=p.

AND

When x=y ≠1 then 3x/y=3=p>2

Note that first formula also gives us the p=3 but only when x and y are the multiples of three (n ANY number but 1, can be -6 or 75 but not 1), thus it exclude all possibilities when x=y and ARE not multiples of three, for instance x=8 and y=8.

So from above it's not necessary x=y or y=1 or x,y to be primes.

Let's look:

I. x = y --> not necessarily true: x=25 y=15 3x/y=5

II. y=1 --> not necessarily true: x=8 y=8 3x/y=3

III. x and y are prime integers --> x=21 y=9 3x/y=7
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I got A picking x=16 and y=6..we get 3x/y = 7....thus OA A
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Bhushan S.
If you like my post....Consider it for Kudos

I'm assuming that the question reads ... and x is a prime integer greater than 2.

In these questions, always start with III

III. x and y are prime integers.
Well x is a prime integer. But y could be any number other than 3. NOT TRUE.

II. y = 1. Need not be true. y could be anything other than 3.

I. x = y. Need not be true. y could be anything other than 3.

Pick A

Rather basic question, doubt you'll see this in the actual test.

First of all the question misses important part (\frac{3x}{y}=prime). Second this question is MUST be true question not COULD be true.

Refer to the solutions above to see that it's not necessary x=y to be true for 3x/y to be a prime integer greater than 2. For example x=25 and y=15 --> \frac{3x}{y}=5=prime.

Hope it's clear.
_________________

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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